Yoonie is a personnel manager in a large corporation. Each month she must review 20 of the employees. From past experience, she has found that the reviews take her approximately 2.5 hours each to do with a population standard deviation of 0.9 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 20 reviews. Assume that the 20 reviews represent a random set of reviews. (a) What is the mean, standard deviation, and sample size? Mean = Number Standard Deviation = Number Sample Size = Number 6. (b) Complete the distributions. Round all decimals to four decimal places. X~ Click for List ( Number , Number X ~ Click for List ( Number Number Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean / = 83 points and standard deviation o = 16 points. Round your answers to one decimal place. The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days (a) Calculate the first- and third-quartile scores for this exam. and a standard deviation of 1.7 days. (a) What is the probability of spending more than four days in recovery? Q1 = Number points Q3 = Number points 7. O 0.7778 0 0.2222 0.5700 10. (b) The middle 50% of the exam scores are between what two values? 0 0.1841 Enter your answers in increasing order The middle 50% of the exam scores are between Number points and Number points. Suppose X ~ N (-2, 2). Between what a values does 68.25% of the data lie? (b) The 90th percentile for recovery times is? 0 6.73 The range of a values is centered at the mean of the distribution (i.e., -2) 0 3.88 8. 7.48 Enter your answers in increasing order, to the nearest integer. 8.49 68.25% of the data lie between Number and Number Based on data from the National Health Survey, women between the ages of 18 and 24 have an average systolic blood pressures (in mm Hg) of 114.9 with a standard deviation of 11.87. Systolic blood pressure for women between the ages of 18 to 24 follow a normal distribution. (a) If one woman from this population is randomly selected, find the probability that her systolic blood pressure is greater than 116 Round your answer to four decimal places P(x > 116) = Number 9. (b) If 35 women from this population are randomly selected, find the probability that their mean systolic blood pressure is greater than 116. Round your answer to four decimal places. P(x > 116) = Number (c) If the sample were four women between the ages of 18 to 24 and we did not know the original distribution, could the central limit theorem be used? O Yes O No
